Depth map obtained from orthographic camera has no white pixels even when there is no object before the far clipping plane
In order to save a render as image, the scene linear values have to be transformed into the chosen display color space. This is what the Display Device and View Transform settings are for in the Color Management panel. However depth information are non-color data that shouldn't be transformed (except for mapping to the value range the image format can store). Therefore you either need to save the image as OpenEXR, which will store the scene linear values or you can choose another format, but then you will have to set the View Transform to Raw. You can find more information about the color management settings in Blender's manual.



Since you don't want to store the actual depth values, but rather normalized values in the range $\left[0,1\right]$ (or $\left[0,255\right]$) you will have to normalize the depth pass. Switch to the compositor and enable Use nodes. Add a Normalize node (Add > Vector > Normalize) and connect the Depth socket with its input Value socket. Connect the output Value socket to the Image socket of the Composite node.



With these settings you should get the expected values in your saved image.